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3 years ago

Is the sequence "109,104,99,94", finite?

Mathematics

1 answer:

Law Incorporation [45]3 years ago

5 0

Answer:

NO.

Step-by-step explanation:

The common difference is -4 and you can continue to add -4 for ever!!

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if the letters of the word 'MOTHER'are written in all possible order and these words are written out as in dictionary ,find the

Marta_Voda [28]

There are 6 letters, each different
Before MOTHER, words from E , H will come
Words from E = 5! (there are 5 letters to arrange)
Words from H = 5!( there are 5 letters to arrange)

Now words starting by M will come.
First ME will have = 4! (as 4 letters will be arranged)
Then MH = 4!
Now words with MO
First words starting with MOE... =3!
And words starting with MOH... =3!
the words starting with MOR... =3!

Now, words starting from MOT will come
words starting with MOTE.. = 2!
then after words starting from MOTH will come and first word will MOTHER

so, total no. of words before MOTHER = 5! + 5! + 2* 4! + 3 * 3!
= 120 +120 + 48 + 18
= 306
so, rank of MOTHER = 307

7 0

3 years ago

Jenny thinks that the expression below is equal to x²-4. If you agree, show that she is correct. If you disagree, show that she

sergiy2304 [10]

Answer:

Jenny is wrong the correct answer is x²+ 4 - 4 x.

Step-by-step explanation:

Given that

(x-2)³∕x-2

(x-2)³∕(x-2) =(x-2) (x-2)²∕(x-2)

(x-2)³∕(x-2) = (x-2)²

As we know that

(a-b)² = a²+b² - 2 ab

(x-2)² = x²+ 2² - 2 ˣ 2 ˣ x = x²+ 4 - 4 x

(x-2)² = x²+ 4 - 4 x

It means that

(x-2)³∕(x-2) = (x-2)² = x²+ 4 - 4 x

So Jenny is wrong the correct answer is x²+ 4 - 4 x.

8 0

2 years ago

A tunnel is built in form of a parabola. The width at the base of tunnel is 7 m. On

uysha [10]

Given:

The width at the base of parabolic tunnel is 7 m.

The ceiling 3 m from each end of the base there are light fixtures.

The height to light fixtures is 4 m.

To find:

Whether it is possible a trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel.

Solution:

The width at the base of tunnel is 7 m.

Let the graph of the parabola intersect the x-axis at x=0 and x=7. It means x and (x-7) are the factors of the height function.

The function of height is:

$h(x)=ax(x-7)$ ...(i)

Where, a is a constant.

The ceiling 3 m from each end of the base there are light fixtures and the height to light fixtures is 4 m. It means the graph of height function passes through the point (3,4).

Putting x=3 and h(x)=4 in (i), we get

$4=a(3)((3)-7)$

$4=a(3)(-4)$

$\dfrac{4}{(3)(-4)}=a$

$-\dfrac{1}{3}=a$

Putting $a=-\dfrac{1}{3}$ , we get

$h(x)=-\dfrac{1}{3}x(x-7)$ ...(ii)

The center of the parabola is the midpoint of 0 and 7, i.e., 3.

The width of the truck is 4 m. If is passes through the center then the truck must m 2 m on the left side of the center and 2 m on the right side of the center.

2 m on the left side of the center is x=1.5.

A trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel is possible if h(1.5) is greater than 2.8.

Putting x=1.5 in (ii), we get

$h(1.5)=-\dfrac{1}{3}(1.5)(1.5-7)$